J. Nonl. Evol. Equ. Appl. 2013 (9), pp. 111-128, published on October 10, 2014:

Approximation of a solution of a semilinear evolution equation with a deviated argument

P. Kumar, D. N. Pandey, D. Bahuguna

Department Of Mathematics And Statistics, Indian Institute Of Technology Kanpur; Kanpur, Uttar Pradesh, India, Pin-208016

Department Of Mathematics, Indian Institute Of Technology Roorkee; Uttarakhand, India, Pin-247667

Received on August 7, 2012
Accepted on November 30, 2012

Communicated by Minh V. Nguyen

Abstract.  In this paper we shall study the approximation of a solution to a classof semilinear evolution equations with a deviated arguments in a separable Hilbert space. With the help of analytic semigroup theory and Banach fixed point theory we shall establish the existence and uniqueness of solutions of the problem considered. Next we consider the Faedo-Galerkin approximation of the solution and prove some convergence results. We illustrate this with an application.
Keywords:Semilinear evolution equation with a deviated arguments, Faedo-Galerkin approximation, Banach fixed point theorem Analytic semigroup.
2010 Mathematics Subject Classification:   34K30, 34G20, 47H06.

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